Details

Time bar (total: 2.8s)

analyze2.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample832.0ms (29.8%)

Results
622.0ms8256×body128valid
Compiler

Compiled 44 to 28 computations (36.4% saved)

simplify86.0ms (3.1%)

Algorithm
egg-herbie
Rules
649×fma-neg_binary64
504×div-sub_binary64
481×fma-def_binary64
326×times-frac_binary64
174×associate-/l/_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11310
22110
33710
46410
511310
621610
741510
875410
9118310
10153710
11161210
12165710
13168410
14169410
15170210
16170210
17160010

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
62.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
62.0b
(/.f64 (-.f64 x lo) (-.f64 hi lo))
Compiler

Compiled 30 to 18 computations (40% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
62.0b
(/.f64 (-.f64 x lo) (-.f64 hi lo))

series21.0ms (0.8%)

Counts
1 → 36
Calls

1 calls:

21.0ms
(/.f64 (-.f64 x lo) (-.f64 hi lo))

rewrite12.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity_binary64
37×add-sqr-sqrt_binary64
25×times-frac_binary64
13×add-cube-cbrt_binary64
12×distribute-lft-out--_binary64
Counts
1 → 54
Calls

1 calls:

8.0ms
(/.f64 (-.f64 x lo) (-.f64 hi lo))

simplify81.0ms (2.9%)

Algorithm
egg-herbie
Rules
810×fma-neg_binary64
418×fma-def_binary64
402×associate--l+_binary64
279×cancel-sign-sub-inv_binary64
264×times-frac_binary64
Counts
90 → 84
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01622093
14362033
213581879
346431879
453461879

prune40.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New80484
Fresh000
Picked101
Done000
Total81485
Error
51.3b
Counts
85 → 4
Alt Table
StatusErrorProgram
52.0b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
58.2b
(-.f64 (+.f64 1 (+.f64 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
52.0b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
Compiler

Compiled 1901 to 683 computations (64.1% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))
0.7b
(pow.f64 (/.f64 lo hi) 3)
1.6b
(+.f64 (/.f64 lo hi) 1)
1.6b
(-.f64 -1 (/.f64 lo hi))

series45.0ms (1.6%)

Counts
4 → 96
Calls

4 calls:

18.0ms
(*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))
16.0ms
(pow.f64 (/.f64 lo hi) 3)
5.0ms
(+.f64 (/.f64 lo hi) 1)
5.0ms
(-.f64 -1 (/.f64 lo hi))

rewrite59.0ms (2.1%)

Algorithm
rewrite-expression-head
Rules
173×add-sqr-sqrt_binary64
164×*-un-lft-identity_binary64
158×add-cube-cbrt_binary64
147×times-frac_binary64
117×prod-diff_binary64
Counts
4 → 293
Calls

4 calls:

13.0ms
(*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))
6.0ms
(-.f64 -1 (/.f64 lo hi))
5.0ms
(+.f64 (/.f64 lo hi) 1)
3.0ms
(pow.f64 (/.f64 lo hi) 3)

simplify195.0ms (7%)

Algorithm
egg-herbie
Rules
621×fma-neg_binary64
480×associate-*l*_binary64
444×associate-*r*_binary64
380×log-prod_binary64
293×*-commutative_binary64
Counts
389 → 340
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04107239
111255197
232834476
342784476
448464476

prune222.0ms (8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3337340
Fresh033
Picked101
Done000
Total33410344
Error
50.8b
Counts
344 → 10
Alt Table
StatusErrorProgram
58.3b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (neg.f64 (pow.f64 (/.f64 lo hi) 2))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (*.f64 (pow.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (*.f64 (cbrt.f64 hi) (cbrt.f64 hi))) 3) (pow.f64 (/.f64 (cbrt.f64 lo) (cbrt.f64 hi)) 3))))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (+.f64 -1 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (sqrt.f64 hi))) (/.f64 (cbrt.f64 lo) (sqrt.f64 hi)))))) (pow.f64 (/.f64 lo hi) 3)))
52.0b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
58.2b
(-.f64 (+.f64 1 (+.f64 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
52.0b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (*.f64 (pow.f64 (*.f64 (cbrt.f64 (/.f64 lo hi)) (cbrt.f64 (/.f64 lo hi))) 3) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 3))))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (+.f64 (*.f64 (/.f64 lo hi) -1) (*.f64 (/.f64 lo hi) (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) 1)) (/.f64 (cbrt.f64 lo) hi))))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (neg.f64 lo) (/.f64 1 hi)) (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
52.2b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (/.f64 (*.f64 lo (-.f64 1 (pow.f64 (/.f64 lo hi) 2))) (*.f64 hi (+.f64 -1 (/.f64 lo hi))))) (pow.f64 (/.f64 lo hi) 3)))
Compiler

Compiled 17809 to 6094 computations (65.8% saved)

localize17.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(pow.f64 (/.f64 lo hi) 3)
0.9b
(*.f64 (neg.f64 lo) (/.f64 1 hi))
1.6b
(+.f64 (/.f64 lo hi) 1)
1.8b
(+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (neg.f64 lo) (/.f64 1 hi)) (/.f64 lo hi)))

series31.0ms (1.1%)

Counts
2 → 48
Calls

2 calls:

24.0ms
(+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (neg.f64 lo) (/.f64 1 hi)) (/.f64 lo hi)))
7.0ms
(*.f64 (neg.f64 lo) (/.f64 1 hi))

rewrite18.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64
13×associate-*r*_binary64
13×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
11×times-frac_binary64
Counts
2 → 68
Calls

2 calls:

8.0ms
(*.f64 (neg.f64 lo) (/.f64 1 hi))
6.0ms
(+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (neg.f64 lo) (/.f64 1 hi)) (/.f64 lo hi)))

simplify81.0ms (2.9%)

Algorithm
egg-herbie
Rules
554×fma-def_binary64
298×cube-prod_binary64
269×times-frac_binary64
246×associate-/l*_binary64
203×exp-prod_binary64
Counts
116 → 108
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01241422
13411180
211571151
342121151
451061151

prune121.0ms (4.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1892191
Fresh279
Picked101
Done000
Total1929201
Error
50.8b
Counts
201 → 9
Alt Table
StatusErrorProgram
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (exp.f64 (+.f64 (log.f64 (neg.f64 lo)) (neg.f64 (log.f64 hi)))) (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (+.f64 -1 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (sqrt.f64 hi))) (/.f64 (cbrt.f64 lo) (sqrt.f64 hi)))))) (pow.f64 (/.f64 lo hi) 3)))
52.0b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
58.2b
(-.f64 (+.f64 1 (+.f64 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
52.0b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
58.3b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (neg.f64 (pow.f64 (/.f64 lo hi) 2))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (*.f64 (pow.f64 (*.f64 (cbrt.f64 (/.f64 lo hi)) (cbrt.f64 (/.f64 lo hi))) 3) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 3))))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (/.f64 (neg.f64 (cbrt.f64 lo)) hi)) (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
52.2b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (/.f64 (*.f64 lo (-.f64 1 (pow.f64 (/.f64 lo hi) 2))) (*.f64 hi (+.f64 -1 (/.f64 lo hi))))) (pow.f64 (/.f64 lo hi) 3)))
Compiler

Compiled 9176 to 3725 computations (59.4% saved)

localize20.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(*.f64 (cbrt.f64 lo) (cbrt.f64 lo))
0.7b
(pow.f64 (/.f64 lo hi) 3)
1.6b
(+.f64 (/.f64 lo hi) 1)
1.8b
(+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (/.f64 (neg.f64 (cbrt.f64 lo)) hi)) (/.f64 lo hi)))

series75.0ms (2.7%)

Counts
2 → 36
Calls

2 calls:

40.0ms
(*.f64 (cbrt.f64 lo) (cbrt.f64 lo))
34.0ms
(+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (/.f64 (neg.f64 (cbrt.f64 lo)) hi)) (/.f64 lo hi)))

rewrite16.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
16×cbrt-prod_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
pow1_binary64
Counts
2 → 62
Calls

2 calls:

6.0ms
(+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (/.f64 (neg.f64 (cbrt.f64 lo)) hi)) (/.f64 lo hi)))
4.0ms
(*.f64 (cbrt.f64 lo) (cbrt.f64 lo))

simplify84.0ms (3%)

Algorithm
egg-herbie
Rules
533×associate-*l/_binary64
491×fma-def_binary64
268×associate-/l*_binary64
223×times-frac_binary64
180×cancel-sign-sub-inv_binary64
Counts
98 → 96
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01061659
12971175
29731072
348951072
450121072

prune102.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1763179
Fresh268
Picked101
Done000
Total1799188
Error
50.8b
Counts
188 → 9
Alt Table
StatusErrorProgram
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)))) (/.f64 (neg.f64 (cbrt.f64 lo)) hi)) (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
52.0b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (exp.f64 (+.f64 (log.f64 (neg.f64 lo)) (neg.f64 (log.f64 hi)))) (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (/.f64 (neg.f64 (cbrt.f64 lo)) hi)) (/.f64 lo hi)))) (*.f64 (pow.f64 (*.f64 (cbrt.f64 (/.f64 lo hi)) (cbrt.f64 (/.f64 lo hi))) 3) (pow.f64 (cbrt.f64 (/.f64 lo hi)) 3))))
58.2b
(-.f64 (+.f64 1 (+.f64 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
52.0b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
58.3b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (neg.f64 (pow.f64 (/.f64 lo hi) 2))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (/.f64 (neg.f64 (cbrt.f64 lo)) hi)) (/.f64 lo hi)))) (cbrt.f64 (+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (/.f64 (neg.f64 (cbrt.f64 lo)) hi)) (/.f64 lo hi))))) (cbrt.f64 (+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (/.f64 (neg.f64 (cbrt.f64 lo)) hi)) (/.f64 lo hi)))))) (pow.f64 (/.f64 lo hi) 3)))
52.2b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (/.f64 (*.f64 lo (-.f64 1 (pow.f64 (/.f64 lo hi) 2))) (*.f64 hi (+.f64 -1 (/.f64 lo hi))))) (pow.f64 (/.f64 lo hi) 3)))
Compiler

Compiled 9205 to 2839 computations (69.2% saved)

regimes424.0ms (15.2%)

Accuracy

Total 1.2b remaining (2.4%)

Threshold costs 0b (0%)

Counts
86 → 1
Compiler

Compiled 16094 to 7540 computations (53.2% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
*-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01544
12144
23044
33644
44044
54144
64144

end186.0ms (6.7%)

Compiler

Compiled 482 to 222 computations (53.9% saved)

Profiling

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